Several different countries have conservative parties; you should state which one you are enquiring about.
There are 8
Conservative Party: Prime Minister David Cameron Labour Party: Ed Milliband LDP: Nick Clegg
The Progressive Conservative Party of Canada was dissolved in 2003.
In Canada West, the leaders of the major political parties included George Brown, who led the Liberal Party, and John A. Macdonald, who was a prominent figure in the Conservative Party. In Canada East, the Liberal Party was led by Antoine-Aimé Dorion, while the Conservative Party was led by George-Étienne Cartier. These leaders played significant roles in the political landscape leading up to Canadian Confederation in 1867.
The Republican Party is the Conservative Party in the US. (Techinally there is no Conservative "Party", but Republicans are considered Conservatives)
The Conservative Party of CanadaStephen Harper is part of the Conservative party and has been from 2003 to present
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The Tory Party, officially known as the Conservative Party in the UK, has had several notable leaders throughout its history. Early leaders included Sir Robert Peel in the 19th century, who is known for founding the modern Conservative Party. Other prominent figures include Winston Churchill, who led during World War II, and Margaret Thatcher, the first female Prime Minister, who served from 1979 to 1990. More recent leaders include David Cameron, Theresa May, and Boris Johnson, each shaping the party's direction in contemporary politics.
He is leader of the UK Conservative party.
In the UK, the Conservative party is the main party at the moment, although Conservative is an ideology which many parties share. So it is both.
The Conservative party, led by Stephen Harper.
Progressive Conservative Party of Canada was created in 1867.